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The probability that someone catches a flu in a month is 1/10. We assume that he can catch the flu only once per month and he is cured by the end of the month he caught the flu. What is the probability that someone catches a flu in two or more of the three months from September through November ?

Teo Protoulis
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Let $X_i=1$ if you catch a flu in month $i$. Then $X_i$ is a bernoullian r.v. with $P(X_i=1) = 1/10$.

Let $Y = X_9+X_{10}+X_{11}$. Then $Y$ is a binomial distribution with parameters $n=3$ and $p=1/10$. So $$P (Y \ge 2) = P (Y = 2) + P (Y = 3) = 3 \left(\frac{1}{10}\right)^2 \left(\frac{9}{10}\right) + \left(\frac{1}{10}\right)^3$$

mlc
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  • Thank you very much for the explanation. One last question. Is there a way that you understood that it is a binomial distribution ? – Teo Protoulis Apr 22 '17 at 14:17
  • @Teo Protoulis: the sum of iid bernoullians is a binomial. You can learn more about this at https://math.stackexchange.com/questions/838107/relationship-between-binomial-and-bernoulli – mlc Apr 22 '17 at 16:07
  • Thank you, this thread about distributions is very helpful. – Teo Protoulis Apr 22 '17 at 16:11